Turbulent Reacceleration of Streaming Cosmic Rays

Subsonic, compressive turbulence transfers energy to cosmic rays (CRs), a process known as non-resonant reacceleration. It is often invoked to explain observed ratios of primary to secondary CRs at $\sim \rm GeV$ energies, assuming wholly diffusive CR transport. However, such estimates ignore the impact of CR self-confinement and streaming. We study these issues in stirring box magnetohydrodynamic (MHD) simulations using Athena++, with field-aligned diffusive and streaming CR transport. For diffusion only, we find CR reacceleration rates in good agreement with analytic predictions. When streaming is included, reacceleration rates depend on plasma $\beta$. Due to streaming-modified phase shifts between CR and gas variables, they are slower than canonical reacceleration rates in low-$\beta$ environments like the interstellar medium (ISM) but remain unchanged in high-$\beta$ environments like the intracluster medium (ICM). We also quantify the streaming energy loss rate in our simulations. For sub-Alfv\'{e}nic turbulence, it is resolution-dependent (hence unconverged in large scale simulations) and heavily suppressed -- by an order of magnitude -- compared to the isotropic loss rate $v_{A} \cdot \nabla P_{\rm CR} / P_{\rm CR} \sim v_{A}/L_{0}$, due to misalignment between the mean field and isotropic CR gradients. Counterintuitively, and unlike acceleration efficiencies, CR losses are almost independent of magnetic field strength over $\beta \sim 1-100$ and are, therefore, not the primary factor behind lower acceleration rates when streaming is included. While this paper is primarily concerned with how turbulence affects CRs, in a follow-up paper (Bustard and Oh, in prep), we consider how CRs affect turbulence by diverting energy from the MHD cascade, altering the pathway to gas heating and steepening the turbulent power spectrum.Comment: 20 pages, 7 figures, comments welcome

Cosmic Ray Drag and Damping of Compressive Turbulence

While it is well-known that cosmic rays (CRs) can gain energy from turbulence via second order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time $t_{\rm damp} \sim \rho v^{2}/\dot{E}_{\rm CR} \propto E_{\rm CR}^{-1}$ becomes comparable to the turbulent cascade time. Magnetohydrodynamic (MHD) simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating at $\dot{E}_{\rm CR} \sim \tilde{\epsilon}$, where $\tilde{\epsilon}$ is the turbulent energy input rate. In that case, almost all the energy in large scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge-Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of $E > 300$ GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large scale motions, with kinetic energy reduced by up to to an order of magnitude in realistic $E_{\rm CR} \sim E_{\rm g}$ scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e. $\tilde{\epsilon} \gg \rho v^{3}/L$.Comment: Accepted to ApJ. Additions include Section 4.5 which shows decomposed solenoidal and compressive spectra, Figure 7 showing CR and magnetic energy spectra, new Figure 3 panel showing modified Burgers spectra, and small corrections to Figure

Cosmic-Ray Drag and Damping of Compressive Turbulence

While it is well known that cosmic rays (CRs) can gain energy from turbulence via second-order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time ${t}_{\mathrm{damp}}\sim \rho {v}^{2}/{\dot{E}}_{\mathrm{CR}}\propto {E}_{\mathrm{CR}}^{-1}$ becomes comparable to the turbulent cascade time. Magnetohydrodynamic simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating at ${\dot{E}}_{\mathrm{CR}}\sim \tilde{\epsilon }$ , where $\tilde{\epsilon }$ is the turbulent energy input rate. In that case, almost all of the energy in large-scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge–Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of E ≳ 300 GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large-scale motions, with kinetic energy reduced by up to 1 order of magnitude in realistic E _CR ∼ E _g scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large-scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e., $\tilde{\epsilon }\gg \rho {v}^{3}/L$